KöMaL 2013 C1162

A circle is drawn over the shorter diagonal $AC$=$a$ of a parallelogram ABCD . The intersections of the circle and the parallelogram form the hexagon AIJCKL , whose sides have lengths $\frac a2$, $b$, $b$, $\frac a2$, $b$, $b$ in this order. Determine the sides and angles of the parallelogram.